This paper aims at sharing some pedagogical implications that emerge from the design and application of an active methodological proposal based on problem solving and on the use of differential calculus as a means to approach the contents of kinematics to promote and facilitate meaningful learning of concepts, procedures, attitudes, principles, and laws that govern kinematics in the course of Physics I for students of engineering at the Universidad del Bío-Bío, Chile. The starting point of this proposal consists of presenting an integrating problem for the contents of kinematics, which are at the very core of the learning unit, and that, in turn, can be divided into a series of more localized problems to deal with the different/various contents of this unit. Research findings suggest that students present a favorable opinion about this proposal, and that these findings seem to point out an influence of the methodological proposal on academic achievement and learning strategies as indicators of meaningful learning as well as the value assigned by the students to this proposal.